document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=947213>Question 947213</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The heights and bases of two geometric shapes are modeled by the expressions shown.\r<BR>\n" );
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document.write( " Triangle: h=3x+2 and b=2x+3\r<BR>\n" );
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document.write( " Parallelogram: h=3x+4 and b=3x+2\r<BR>\n" );
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document.write( " What expression represents the number of units by which the area of the parallelogram is greater than the area of the triangle? <BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #577945 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=577945\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "by definition:<BR>\n" );
document.write( "A parallelogram is a 4-sided figure formed by two pairs of parallel lines.Opposite sides are equal in length and opposite angles have equal measure.\r<BR>\n" );
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document.write( "The area of a parallelogram is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=+b+%2A+h ALIGN=MIDDLE  ALT=\"A+=+b+%2A+h\"   DISABLED_style= \"max-width:90%; height:auto;\" >, the area of a triangle <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=must ALIGN=MIDDLE  ALT=\"must\"   DISABLED_style= \"max-width:90%; height:auto;\" > be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=one-half ALIGN=MIDDLE  ALT=\"one-half\"   DISABLED_style= \"max-width:90%; height:auto;\" > the area of a parallelogram. <BR>\n" );
document.write( "Thus, the formula for the area of a triangle is: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=+%281%2F2%29b+%2A+h ALIGN=MIDDLE  ALT=\"A+=+%281%2F2%29b+%2A+h\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "if given\r<BR>\n" );
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document.write( "Triangle: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=3x%2B2 ALIGN=MIDDLE  ALT=\"h=3x%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=2x%2B3 ALIGN=MIDDLE  ALT=\"b=2x%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "then \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5Bt%5D+=+b+%2A+h ALIGN=MIDDLE  ALT=\"A%5Bt%5D+=+b+%2A+h\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5Bt%5D+=+%281%2F2%29%282x%2B3%29%2A%283x%2B2%29 ALIGN=MIDDLE  ALT=\"A%5Bt%5D+=+%281%2F2%29%282x%2B3%29%2A%283x%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5Bt%5D+=+%281%2F2%29%2A%286x%5E2%2B4x%2B9x%2B6%29 ALIGN=MIDDLE  ALT=\"A%5Bt%5D+=+%281%2F2%29%2A%286x%5E2%2B4x%2B9x%2B6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5Bt%5D+=+%281%2F2%29%2A%286x%5E2%2B13x%2B6%29 ALIGN=MIDDLE  ALT=\"A%5Bt%5D+=+%281%2F2%29%2A%286x%5E2%2B13x%2B6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5Bt%5D+=+3x%5E2%2B6.5x%2B3 ALIGN=MIDDLE  ALT=\"A%5Bt%5D+=+3x%5E2%2B6.5x%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "and<BR>\n" );
document.write( " Parallelogram: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=3x%2B4 ALIGN=MIDDLE  ALT=\"h=3x%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=3x%2B2 ALIGN=MIDDLE  ALT=\"b=3x%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5Bp%5D+=+%283x%2B2%29%2A%283x%2B4%29 ALIGN=MIDDLE  ALT=\"A%5Bp%5D+=+%283x%2B2%29%2A%283x%2B4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+%5Bp%5D=+9x%5E2%2B12x%2B6x%2B8 ALIGN=MIDDLE  ALT=\"A+%5Bp%5D=+9x%5E2%2B12x%2B6x%2B8\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5Bp%5D+=+9x%5E2%2B18x%2B8 ALIGN=MIDDLE  ALT=\"A%5Bp%5D+=+9x%5E2%2B18x%2B8\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "What expression represents the number of units by which the area of the parallelogram is greater than the area of the triangle?\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5Bt%5D+=+3x%5E2%2B6.5x%2B3 ALIGN=MIDDLE  ALT=\"A%5Bt%5D+=+3x%5E2%2B6.5x%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5Bp%5D+=+9x%5E2%2B18x%2B8 ALIGN=MIDDLE  ALT=\"A%5Bp%5D+=+9x%5E2%2B18x%2B8\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "find the difference:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5Bp%5D-A%5Bt%5D+=9x%5E2%2B18x%2B8-%283x%5E2%2B6.5x%2B3%29 ALIGN=MIDDLE  ALT=\"A%5Bp%5D-A%5Bt%5D+=9x%5E2%2B18x%2B8-%283x%5E2%2B6.5x%2B3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5Bp%5D-A%5Bt%5D+=9x%5E2%2B18x%2B8-3x%5E2-6.5x-3 ALIGN=MIDDLE  ALT=\"A%5Bp%5D-A%5Bt%5D+=9x%5E2%2B18x%2B8-3x%5E2-6.5x-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5Bp%5D-A%5Bt%5D+=6x%5E2%2B11.5x%2B5 ALIGN=MIDDLE  ALT=\"A%5Bp%5D-A%5Bt%5D+=6x%5E2%2B11.5x%2B5\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x%5E2%2B11.5x%2B5 ALIGN=MIDDLE  ALT=\"6x%5E2%2B11.5x%2B5\"   DISABLED_style= \"max-width:90%; height:auto;\" >=> expression represents the number of units by which the area of the parallelogram is greater than the area of the triangle\r<BR>\n" );
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